Triunitary quantum circuits
Abstract
We introduce a novel class of quantum circuits that are unitary along three distinct ``arrows of time''. These dynamics share some of the analytical tractability of ``dualunitary'' circuits, while exhibiting distinctive and richer phenomenology. We find that twopoint correlations in these dynamics are strictly confined to three directions in $(1+1)$dimensional spacetime  the two light cone edges, $\delta x=\pm v\delta t$, and the static worldline $\delta x=0$. Along these directions, correlation functions are obtained exactly in terms of quantum channels built from the individual gates that make up the circuit. We prove that, for a class of initial states, entanglement grows at the maximum allowed speed up to an entropy density of at least one half of the thermal value, at which point it becomes modeldependent. Finally, we extend our circuit construction to $2+1$ dimensions, where twopoint correlation functions are confined to the onedimensional edges of a tetrahedral light cone  a subdimensional propagation of information reminiscent of ``fractonic'' physics.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.07686
 Bibcode:
 2021arXiv210607686J
 Keywords:

 Quantum Physics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory
 EPrint:
 11 pages main text + 2 page appendix, 15 figures